Fermions, Mass-Gap and Landau Levels: Gauge invariant Hamiltonian for QCD in D=2+1

TL;DR

This paper develops a gauge-invariant Hamiltonian formulation of 3D QCD including fermions, computes the fermionic effects on the volume element and mass gap, and relates these to topological and confinement phenomena.

Contribution

It introduces a consistent method for incorporating fermions into gauge-invariant Hamiltonian QCD in 2+1 dimensions and computes their impact on the volume element and mass gap.

Findings

Exact computation of fermionic contribution to the volume element.

Relation of fermionic effects to Chern-Simons term induction.

Consistency with index theorems, Landau Levels, and renormalization results.

Abstract

A gauge-invariant reformulation of QCD in three spacetime dimensions is presented within a Hamiltonian formalism, extending previous work to include fermion fields in the adjoint and fundamental representations. A priori there are several ways to define the gauge-invariant versions of the fermions; a consistent prescription for choosing the fermionic variables is presented. The fermionic contribution to the volume element of the gauge orbit space and the gluonic mass-gap is computed exactly and this contribution is shown to be closely related to the mechanism for induction of Chern-Simons terms by parity-odd fermions. The consistency of the Hamiltonian scheme with known results on index theorems, Landau Levels and renormalization of Chern-Simons level numbers is shown in detail. We also comment on the fermionic contribution to the volume element in relation to issues of confinement and screening.